I can only comment on Becky High and cannot give a comparison as I don't have first hand experience of the other schools. Best of luck with your decision!
My oldest daughter is happy at Becky High and her sister will be joining her there hopefully next September. I have only good things to say about the school. Not everything is perfect but where is? A strong point for me is the current Head - she is fantastic and a good leader.
I will try and answer your more specific Qs below, at least from my persepctive.
My daughter is not sporty but did participate in extra curricular dance activities up until this year. Standard of sports like netball, hockey, running, dance etc is high but I don't see a problem with that. Everyone has their strengths and weaknesses. There are lots of sports clubs as well as teams for those who want to participate.
Happens at every school whether single sex, GS or not - there are those who are not so nice and those that are lovely. My daughter has some wonderful friends but they are not all like that. Sorry to hear of the experience of your friend
Generally very good in our experience. My daughter hasn't had much swapping around but she is older so maybe they try and minimise impact?
My daughter is into drama and has particpated in every opportunity in that area. Currently "Grease" (joint with The Beaconsfield School), The Tempest and the House pantos which are great fun!